In outline then this paper is as follows. We begin in Section 2
with a review of some of the more elementary material from
[1]} on the category \({K}/B\)  of \(k\) -spaces over a
fixed compactly generated space \(B\) . We review the
fiberwise model structure (or \(f\) -model structure) on \({K}/B\) , this is
in a certain sense the natural generalization of the classical Strøm model
structure [2]} on topological spaces to the parametrized
setting. We study the notion of group object in \({K}/B\)  and the
corresponding equivariant fiberwise notions of homotopy equivalence,
cofibration and fibration.
